Have you looked into the railway lines? (they don't by any means go everywhere, but some lines - above all the West Highland line, from Glasgow to Oban, or Fort William and Mallaig) are very scenic, if slow.
Also, there are fairly decent networks of coaches in most parts of the country (useful for getting from one railway line to another - eg Inverness to Fort William), mostly run by the companies Scottish Cityline or Stagecoach - all the timetables are on line on their websites.
Nearer to Edinburgh the coast of North-East Fife (from the Tay Bridge round to St Andrews - which is a stunning medieval university town as well as the home of golf, etc) and then to Crail (medieval, gorgeous arty village), Anstruther (famous for its fantastic fish and chip restaurant), St Monans, Pittenweem, and Elie and Earlsferry (a favourite holiday resort of Queen Victoria) is stunning, and relatively little known. Also substantially more likely to be warmer, drier, and not covered in snow than anywhere further West. (The southern part of Fife is mostly less charming, but there are still some nice coastal villages - the railway line between Edinburgh and Dundee goes through a few of them in the first few miles after it crosses the Forth Bridge). Inland Fife is hilly and green rather than mountainous - but really December is not the best time of year to try getting about the highest parts of Scotland...
